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NEW YORK — For Clay Buchholz, Yankee Stadium is his greatest challenge as a pitcher. But not necessarily because of Robinson Cano, Alex Rodriguez, and Mark Teixeira. It’s the other people he’s worried about.

“You have all the fans out there, they all hate us,’’ he said. “It’s tough sometimes.’’

That made last night’s game in the Bronx a true test of whether Buchholz had overcome a rocky April and was again the pitcher who became an All-Star last season. Quality starts against the Angels and Twins, while helpful, were not truly indicative.

Now he has validation, throwing seven strong innings that propelled the Red Sox to a 5-4 victory.

Adrian Gonzalez and Kevin Youkilis homered as the Red Sox improved to 3-1 against their rivals this season.

Buchholz allowed two runs on five hits, with one walk and seven strikeouts. The seven innings were his most this season, as were the 110 pitches he threw.

After starting their road trip with two disheartening losses in Toronto, the Sox got exactly what they needed from Buchholz.

“He was tremendous,’’ manager Terry Francona said. “He was really good. He threw hard and down with movement, then he started using his changeup and breaking ball. His fastball had so much depth to it and it had real good velocity. That was impressive.’’

Buchholz had one victory and a 6.25 earned run average in six previous appearances against the Yankees. That included giving up four earned runs over 3 2/3 innings April 9 at Fenway Park.

But he overmatched the Yankees at times last night, consistently throwing his fastball for strikes and mixing in secondary pitches to cause a flurry of bad swings.

“His velocity was as good as we’ve seen in a long time. He got up to 98 in the first or second inning. He sunk it well, threw good cutters,’’ Rodriguez said.

Buchholz sailed through the first four innings, putting three runners on base. To that point, Buchholz had thrown only 61 pitches and the Yankees had swung and missed 15 times.

That changed in the fifth inning. Buchholz fell behind Jorge Posada then left a fastball over the plate that was lined into right field. The first pitch to Russell Martin was a cutter that stayed out over the plate. Martin extended his arms and drove the ball over the fence in center.

Brett Gardner followed with a third consecutive hit, a single to center. But Buchholz got Derek Jeter on a ground ball and Curtis Granderson on a fly ball to center before striking out Teixeira on a changeup.

“I just didn’t want to give in. I wanted them to hit a good pitch,’’ Buchholz said.

Buchholz has given up only four earned runs over his last 18 2/3 innings with 15 strikeouts.

“He hit my glove wherever I put it the last two games,’’ catcher Jarrod Saltalamacchia said. “Everything is moving.’’

Buchholz (4-3) turned a 5-2 lead over to Daniel Bard. The usually reliable setup man had little control, throwing only 13 of 28 pitches for strikes. But he got through the inning allowing just one run.

Granderson started the inning with a triple then scored on a wild pitch. Rodriguez walked before Bard hit Cano in the left foot.

After a double steal, Bard struck out Nick Swisher with a 99-mile-per-hour fastball and got Posada to ground to second

Jonathan Papelbon finished the Yankees off in the ninth inning for his sixth save, giving up a run after getting two outs. New York has dropped seven of its last 10 games.

Bartolo Colon made his first start against the Sox since 2005 and pitched well, allowing three runs (two earned) over six-plus innings.

The Red Sox got to him in the fourth inning. Gonzalez led off by pulling a fastball into the second deck in right field for his eighth home run of the season. It was the sixth home run in a span of 29 at-bats for Gonzalez, who was playing at the new Yankee Stadium for the first time.

“That guy makes everyone around him better,’’ Dustin Pedroia said.

Colon came back to strike out Youkilis, but the ball got past Martin and Youkilis reached first. David Ortiz drew a walk before J.D. Drew grounded into a force play that sent Youkilis to third.

Carl Crawford grounded to first base to drive in the run as the Sox went ahead, 2-0.

The Sox made it 5-2 in the seventh. With Jacoby Ellsbury on first and one out, Francona called for a hit-and-run against Joba Chamberlain and Pedroia grounded a single through the spot vacated by Cano at second base. Ellsbury took third.

“That’s good hitting,’’ Francona said. “It’s nice to see us do things like that.’’

Gonzalez was the right man at the right time and delivered a sacrifice fly to left field, taking a good swing at a 2-and-2 fastball and driving the ball to fence.

Youkilis followed with a home run to right-center.

“I was very fortunate we’re not playing at Fenway Park,’’ Youkilis said. “The ball travels to right field here. It’s an out at Fenway Park.’’